Since the anime isn't done, I would say start with the manga, then watch all the anime. The anime is really good. You could also watch all of the currently released anime, then read the rest of the manga (That's my personal choice).
What i did was to watch the whole anime first (but this was when it was only 2 seasons of Dr. Stone and it wasn’t ongoing) and then I read the remaining stuff.
Both the show and the anime are aligned with everything. so def recommend the anime. But if you feel impatient waiting for the next episodes to release or feel it's going too slow then you're free to pick up the manga if you wanna know what happens or go at your own pace. I Also recommend reading through the official fan book if ya wanna get a good idea of everyone;s timeline in the series.
